Abstract
We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models, the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. Our main interest here is to use this freedom to compute various topological invariants for surfaces, such as the intersection numbers for curves drawn on a surface of given genus with marked points, or the P^1 Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. We have presented most results in several earlier publications, but here we have attempted to present a unified and concise exposition.
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